APPLICATION OF LATTICE GAS AUTOMATA TO PETROLEUM ENGINEERING

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APPLICATION OF LATTICE GAS AUTOMATA TO PETROLEUM
ENGINEERING

• What is it?
• What we are doing.
• What we are going to do.

Assoc. Professor Dr. Mariyamni Awang UTM/PRSS
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PARTICLE MOVEMENTS NAVIER STOKES EQUATION

• Particles moving within a given
  structure(lattice) are used to represent fluid
  flow.
• Reported in mathematical journals before the 80s
  but flow in porous media was studied since then.
• The first model did not satisfy the NS equation

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First model Four sided lattice, HPP (Hardy,de
Pazzis,Pomeau)
particle
Bigger than a molecule
node
link
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TWO STEPS

• The particles undergo two processes
• Propagation unit mass particle moving at unit
  speed in a given direction, along a link
  (connection between two nodes). It reaches a
  neighbouring node in one time step
• Collision occurs under a set of collision rules
  and exclusion rules. Only one particle is allowed
  to travel in the same direction along a link.

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EXCLUSION RULES
-Maximum of 4 particles to a node at any time,
each one will have a different direction of
movement. - Collision rules result in momentum
and mass being conserved at each node
Againstexc. rule
In
Out
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MODELS THAT WORK
FHP models
Hexagonal Lattice model satisfies NS equation
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FHP MODELS

• 1986 Frisch,Hasslacher and Pomeau used the
  hexagonal lattice
• Most of the rules for the HPP were maintained and
  unlike the HPP, the Navier Stokes equation was
  satisfied without introducing any extra term

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MOVEMENT OF PARTICLESFHP 1

• Maximum of six particles to a lattice (for a
  hexagon), each particle is of unit mass
• Particles collide and move to the neighbouring
  node within one time step
• The movement takes place along a link and all
  particles move at equal speed.
• If no collision occurs, movement continues along
  the link

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RULES

• Exclusion rules
• Eg Only 1 particle per direction at each node
• 2) Collision rules
• Eg Particles only collide at the node
• 3) Conservation of mass and momentum

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COLLISION RULES
Examples
OR
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FHP II MODEL

• A rest particle is introduced to allow more
  flexibility.
• Another rule is addednormal particles can
  convert to rest particles upon collision

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OTHER MODELS

• FHP III model conserves momentum, allows more
  combinations
• Face centered hypercube lattice for 3 D
  modelling. The collision and exclusion rules are
  modified from FHP models

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MORE COLLISION RULES
2 PARTICLES? 1 REST, 1 PARTICLE
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UPSCALING

• - Particles at the microscopic scale, continuum
  at the macroscopic scale.

- Macroscopic relationships used are density
,viscosity and pressure to relate to NS Eg
density per node Snumber of particles

• All of the equations have been derived by various
  
• mathematicians

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LGA Equations, FHP I
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WHY LGA?

• Parallel behaviour
• Outcome of the collisions are not dependent on
  the neighbours entirely
• No floating point calculations
• Logical ifs only
• New interesting area

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DISADVANTAGES

• Large memory required due to the lattice size,
  typical PC allows 300x500 lattices to be
  modelled. Node to node distance (O) 1 mm
• Incompressible flow only (NV)
• 3D flow has been not been modelled successfully

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REPORTED RESEARCH

• Permeabilities calculated compared with
  laboratory measurements were acceptable
• Several effects, such as two fluid flow,flow
  around obstacles, were reported
• Different macroscopic equations were used

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PERMEABILITY
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CURRENT INVESTIGATIONS

• Single phase, 1 D gas flow
• Prediction of permeability for a wide range of
  permeability. To be compared with lab results,
  core and micromodel.
• Problem of representing the physical model on
  microscopic level

Rest particles represent Sand grain
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CURRENT INVESTIGATIONS

• K studies Study the effects of sand grain
  distribution, density of fluids, size of
  lattice,tortuosity and several boundary
  conditions
• Two phase displacements lighter particles
  displacing heavy particles.

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FUTURE
-Polymer injection with adsorption effects, dead
end effects. - Cray computer will be used to
increase the size of the model
Application to full scale simulation a la FD
method is not expected in the near future, but
it seems be useful for studies on specific fluid
behaviour and rock characterisation eg
adsorption,capillary flow, diffusion